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Approximating Markov chain occupancy...

Chestnut, Stephen.

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Approximating Markov chain occupancy distributions.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Approximating Markov chain occupancy distributions./
Author:	Chestnut, Stephen.
Description:	45 p.
Notes:	Source: Masters Abstracts International, Volume: 49-01, page: 0476.
Contained By:	Masters Abstracts International49-01.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1481128
ISBN:	9781124222127

Approximating Markov chain occupancy distributions.
Chestnut, Stephen.

Approximating Markov chain occupancy distributions. - 45 p.

Source: Masters Abstracts International, Volume: 49-01, page: 0476.

Thesis (M.S.)--University of Colorado at Boulder, 2010.

Given a homogeneous Markov chain, X, with finite but potentially large state space, S , and a set of states, T ⊂ S , what is the distribution of Tn, the number of times the chain occupies a state in T during the first n steps?

ISBN: 9781124222127Subjects--Topical Terms:

1669109
Applied Mathematics.

Approximating Markov chain occupancy distributions.
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020 $a 9781124222127
035 $a (UMI)AAI1481128
035 $a AAI1481128
040 $a UMI $c UMI
100 1 $a Chestnut, Stephen. $3 1681756
245 1 0 $a Approximating Markov chain occupancy distributions.
300 $a 45 p.
500 $a Source: Masters Abstracts International, Volume: 49-01, page: 0476.
500 $a Adviser: Manuel E. Lladser.
502 $a Thesis (M.S.)--University of Colorado at Boulder, 2010.
520 $a Given a homogeneous Markov chain, X, with finite but potentially large state space, S , and a set of states, T ⊂ S , what is the distribution of Tn, the number of times the chain occupies a state in T during the first n steps?
520 $a The distribution of Tn is the n-step occupancy distribution of X in T. This thesis proposes a new method for approximating this distribution. Our results may be applicable to pattern problems in Markovian and non-Markovian sequences.
520 $a The distribution of Tn can be computed exactly using one-step or transfer matrix methods. Unfortunately, these methods become computationally intractable as n or | S | increase. Normal, Poisson, and compound Poisson approximations to the distribution of Tn have been proposed but may not be accurate for a range of n beyond the applicability of one-step or transfer matrix methods.
520 $a This thesis attempts to bridge the gap between explicit computation and asymptotic approximation of occupancy distributions. We approach the problem with a new interpretation of Doeblin's ergodicity coefficient that allows us to decompose the original chain into an i.i.d. sequence and a remainder chain. The decomposition yields a stochastic process equivalent to the original chain: a coin is tossed before each transition and the new state is chosen from the i.i.d. sequence or the remainder chain, based on the outcome of the toss. The i.i.d. sequence breaks the memory length of the chain and limits the dependence to relatively few transitions governed by the remainder chain. Well known results from the theory of runs in Bernoulli sequences allow us to approximate a chain of duration n by independent realizations of the remainder chain with duration O (log n). We obtain an approximation to the occupancy distribution with a sharp upper-bound on the error, and we test the accuracy of our method via numerical examples.
590 $a School code: 0051.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Statistics. $3 517247
690 $a 0364
690 $a 0463
710 2 $a University of Colorado at Boulder. $b Applied Mathematics. $3 1030307
773 0 $t Masters Abstracts International $g 49-01.
790 1 0 $a Lladser, Manuel E., $e advisor
790 1 0 $a Corcoran, Jem $e committee member
790 1 0 $a Dougherty, Anne $e committee member
790 $a 0051
791 $a M.S.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=1481128